Georgia Institute of Technology College of Sciences

Strong edge coloring of a graph $G$ is a coloring of the edges of the graph such that each color class is an induced subgraph. The strong chromatic index of $G$ is the smallest number $k$ such that $G$ has a $k$-strong edge coloring. Erdős and Nešetřil conjecture that the strong chromatic index of a graph of max degree $\Delta$ is at most $5\Delta^2/4$ if $\Delta$ is even and $(5\Delta^2-2\Delta + 1)/4$ if $\Delta$ is odd. It is known for $\Delta=3$ that the conjecture holds, and in this talk I will present part of Anderson's proof that the strong chromatic index of a subcubic planar graph is at most $10$